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We consider the generic problem of Secure Aggregation of DistributedInformation (SADI), where several agents acting as a team have informationdistributed among them, modeled by means of a publicly known deck of cardsdistributed among the agents, so that each of them knows only her cards. Theagents have to exchange and aggregate the information about how the cards aredistributed among them by means of public announcements over insecurecommunication channels, intercepted by an adversary "eavesdropper", in such away that the adversary does not learn who holds any of the cards. We present acombinatorial construction of protocols that provides a direct solution of aclass of SADI problems and develop a technique of iterated reduction of SADIproblems to smaller ones which are eventually solvable directly. We show thatour methods provide a solution to a large class of SADI problems, including allSADI problems with sufficiently large size and sufficiently balanced carddistributions.

Secure aggregation of distributed information: How a team of agents can safely share secrets in front of a spy